Review for final - Math for business | Trường Đại học Quốc tế, Đại học Quốc gia Thành phố HCM

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Môn: Math for business

Trường: Trường Đại học Quốc tế, Đại học Quốc gia Thành phố Hồ Chí Minh

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Profile Mai Nguyệt
REVIEW FOR FINAL
Problem 1: Given the demand equation and supply equation .
a) Assuming pure competition, find the consumer surplus and producer surplus.
b) Suppose the government decides to impose a tax $5 per unit of good. Work out new PS and
CS.
Determine the change in total surplus of whole economy.
Problem 2: A firm is allowed to charge different prices for its domestic and industrial
customers. If P and Q denote the price and demand for the domestic market then the demand
1 1
equation is . If P and Q denote the price and demand for the industrial market then
2 2
the demand equation is . Total cost function is given by . Find the
price of each market that the firm should charge to maximise profit.
Problem 3: An individual9s utility function is given where x and x denote the number
1 2
of items of two goods, pizza and pasta, respectively. The prices of the goods are $10 and $2,
respectively. Assuming that the individual has $100 to spend on these goods. Find the number of
pizza or pasta dishes to maximize utility function.
Problem 4: During Covid-19 period, company A decides to launch two new products, hand-gel
and face mask. The cost of making each bottle is $16 and the cost for each face mask is $12. The
company recognizes that this is a risky venture so decides to limit the total weekly production costs
to $400. Also, due to a shortage of skilled labor, the total number of products that the company
can produce in a week is at most 30. In market, the selling price of each hand-gel bottle is $23 and
$18 for each face mask.
a) How should the company arrange production to maximize profit?
b) Suppose the president of IU offers from company A to provide anti-infected items for students.
The school9s budget is $8024. They found that the quantity of face mask needs to be larger as
twice as that of the hand-gel bottle because of the frequency of usage. By using the matrix method,
find the number of each type that IU orders.
50 2
D
P Q= -
10 2
S
P Q= +
1 1
20 2P Q= -
2 2
15 1.5P Q= -
1 2
5( )TC Q Q= +
1 2
U x x=
| 1/1
| | Tải xuống

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REVIEW FOR FINAL
Problem 1: Given the demand equation P 50 2 =
- Q and supply equation P 10 2 = + Q . D S
a) Assuming pure competition, find the consumer surplus and producer surplus.
b) Suppose the government decides to impose a tax $5 per unit of good. Work out new PS and CS.
Determine the change in total surplus of whole economy.
Problem 2: A firm is allowed to charge different prices for its domestic and industrial
customers. If P1 and Q1 denote the price and demand for the domestic market then the demand equation is 20 2 P = - Q . If P 1 1
2 and Q2 denote the price and demand for the industrial market then the demand equation is 15 1.5 P = -
Q . Total cost function is given by TC = 5(Q + Q ). Find the 2 2 1 2
price of each market that the firm should charge to maximise profit.
Problem 3: An individual9s utility function is given U x x =
where x1 and x2 denote the number 1 2
of items of two goods, pizza and pasta, respectively. The prices of the goods are $10 and $2,
respectively. Assuming that the individual has $100 to spend on these goods. Find the number of
pizza or pasta dishes to maximize utility function.
Problem 4: During Covid-19 period, company A decides to launch two new products, hand-gel
and face mask. The cost of making each bottle is $16 and the cost for each face mask is $12. The
company recognizes that this is a risky venture so decides to limit the total weekly production costs
to $400. Also, due to a shortage of skilled labor, the total number of products that the company
can produce in a week is at most 30. In market, the selling price of each hand-gel bottle is $23 and $18 for each face mask.
a) How should the company arrange production to maximize profit?
b) Suppose the president of IU offers from company A to provide anti-infected items for students.
The school9s budget is $8024. They found that the quantity of face mask needs to be larger as
twice as that of the hand-gel bottle because of the frequency of usage. By using the matrix method,
find the number of each type that IU orders.